Combinatorial auctions, which allow agents to bid directly for bundles of resources, are necessary for optimal auction-based solutions to resource allocation problems with agents that have non-additive values for resources, such as distributed scheduling and task assignment problems. We introduce iBundle, the first iterative combinatorial auction that is optimal for a reasonable agent bidding strategy, in this case myopic best-response bidding. Its optimality is proved with a novel connection to primal-dual optimization theory. We demonstrate orders of magnitude performance improvements over the only other known optimal combinatorial auction, the Generalized Vickrey Auction.

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